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Steel Designers' Manual - 6th Edition (2003)
UNIVERSAL BEAMS
Dimensions and properties 1171
REDUCED PLASTIC MODULUS UNDER AXIAL LOAD
XIX
Section Plastic Major Axis Reduced Modulus Plastic Minor Axis Reduced Modulus
Designation Modulus
Modulus
Axis
x-x
Lower Values
of n
Change
Formula
Higher Values
of n
Axis
y-y
Lower Values
of n
Change
Formula
Higher Values
of n
At n =
At n =
cm3 K1 K2 K3 K4 cm3 K1 K2 K3 K4
457 ¥ 191 ¥ 98 2230 2230 3440 0.390 203 13.4 379 379 84.0 0.425 1000 0.207
457 ¥ 191 ¥ 89 2010 2010 3080 0.395 169 14.6 338 338 69.8 0.428 914 0.194
457 ¥ 191 ¥ 82 1830 1830 2760 0.406 143 15.8 304 304 59.3 0.436 853 0.172
457 ¥ 191 ¥ 74 1650 1650 2490 0.407 118 17.4 272 272 49.0 0.435 772 0.167
457 ¥ 191 ¥ 67 1470 1470 2150 0.425 96.3 19.1 237 237 40.3 0.451 720 0.128
457 ¥ 152 ¥ 82 1810 1810 2600 0.430 176 12.8 240 240 58.7 0.468 723 0.123
457 ¥ 152 ¥ 74 1630 1630 2320 0.435 145 14.1 213 213 48.3 0.469 656 0.111
457 ¥ 152 ¥ 67 1450 1450 2030 0.450 119 15.5 187 187 40.0 0.482 610 0.0786
457 ¥ 152 ¥ 60 1290 1290 1790 0.455 95.0 17.2 163 163 32.0 0.483 546 0.0670
457 ¥ 152 ¥ 52 1100 1100 1460 0.488 72.9 19.6 133 133 24.7 0.513 509 -0.00290
406 ¥ 178 ¥ 74 1500 1500 2350 0.383 124 14.7 267 267 54.1 0.415 698 0.216
406 ¥ 178 ¥ 67 1350 1350 2080 0.392 102 16.1 237 237 44.7 0.421 640 0.196
406 ¥ 178 ¥ 60 1200 1200 1850 0.393 82.3 17.9 209 209 36.0 0.420 572 0.190
406 ¥ 178 ¥ 54 1060 1060 1540 0.425 66.9 19.8 178 178 29.5 0.450 545 0.124
406 ¥ 140 ¥ 46 888 888 1260 0.442 60.5 18.6 118 118 21.3 0.468 384 0.0864
406 ¥ 140 ¥ 39 724 724 963 0.491 43.5 21.7 90.8 90.8 15.5 0.513 358 -0.0176
356 ¥ 171 ¥ 67 1210 1210 2010 0.353 105 13.7 243 243 50.3 0.387 582 0.272
356 ¥ 171 ¥ 57 1010 1010 1630 0.371 76.4 16.0 199 199 36.8 0.400 506 0.234
356 ¥ 171 ¥ 51 896 896 1420 0.379 61.4 17.8 174 174 29.7 0.405 458 0.215
356 ¥ 171 ¥ 45 775 775 1170 0.405 48.0 20.0 147 147 23.4 0.429 423 0.158
356 ¥ 127 ¥ 39 659 659 938 0.440 49.1 16.9 89.1 89.1 17.5 0.469 289 0.0836
356 ¥ 127 ¥ 33 543 543 740 0.473 35.4 19.8 70.3 70.3 12.7 0.497 261 0.0120
305 ¥ 165 ¥ 54 846 846 1500 0.325 70.8 14.1 196 196 38.1 0.357 431 0.330
305 ¥ 165 ¥ 46 720 720 1290 0.323 52.1 16.3 166 166 28.1 0.350 366 0.331
305 ¥ 165 ¥ 40 623 623 1100 0.331 39.9 18.5 142 142 21.7 0.355 323 0.312
305 ¥ 127 ¥ 48 711 711 1040 0.416 74.8 11.7 116 116 30.1 0.457 335 0.146
305 ¥ 127 ¥ 42 614 614 891 0.424 57.4 13.3 98.4 98.4 23.2 0.460 295 0.127
305 ¥ 127 ¥ 37 539 539 784 0.426 45.1 14.9 85.4 85.4 18.3 0.458 260 0.119
305 ¥ 102 ¥ 33 481 481 663 0.459 42.7 14.3 60.0 60.0 14.0 0.493 202 0.0576
305 ¥ 102 ¥ 28 403 403 536 0.487 31.6 16.5 48.5 48.5 10.4 0.516 183 -0.00120
305 ¥ 102 ¥ 25 342 342 431 0.534 24.6 18.6 38.8 38.8 8.18 0.560 178 -0.100
254 ¥ 146 ¥ 43 566 566 1040 0.308 50.9 13.0 141 141 28.9 0.341 295 0.366
254 ¥ 146 ¥ 37 483 483 883 0.313 38.0 14.9 119 119 21.7 0.342 255 0.353
254 ¥ 146 ¥ 31 393 393 656 0.354 26.9 17.5 94.1 94.1 15.7 0.380 229 0.267
254 ¥ 102 ¥ 28 353 353 517 0.420 31.8 13.8 54.8 54.8 12.5 0.455 163 0.133
254 ¥ 102 ¥ 25 306 306 428 0.450 25.2 15.4 46.0 46.0 9.98 0.482 153 0.0686
254 ¥ 102 ¥ 22 259 259 344 0.489 19.3 17.4 37.3 37.3 7.73 0.517 144 -0.0136
203 ¥ 133 ¥ 30 314 314 570 0.314 27.3 13.5 88.2 88.2 17.7 0.346 190 0.346
203 ¥ 133 ¥ 25 258 258 448 0.334 19.2 15.9 70.9 70.9 12.6 0.362 164 0.300
203 ¥ 102 ¥ 23 234 234 400 0.339 21.2 13.1 49.8 49.8 10.6 0.373 116 0.288
178 ¥ 102 ¥ 19 171 171 307 0.321 14.5 13.8 41.6 41.6 8.28 0.352 93.1 0.318
152 ¥ 89 ¥ 16 123 123 229 0.303 11.6 12.3 31.2 31.2 6.77 0.337 67.0 0.344
127 ¥ 76 ¥ 13 84.2 84.2 171 0.271 8.98 10.7 22.6 22.6 5.37 0.308 44.9 0.399
n = F/(A p y), where F is the factored axial load, A is the gross cross sectional area and py is the design strength of the section.
For lower values of n, the reduced plastic modulus, S r = K1 - K2.n 2 , for both major and minor axis bending.
For higher values of n, the reduced plastic modulus, S r = K3(1 - n)(K4 + n), for both major and minor axis bending.